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Full text of "Mathematical And Physical Papers - Iii"

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Suppose now that the system is at rest and that the disturbing force begins to act. A motion will be prcxlueed gradually tending to become that permanent kind of motion above referred to. If the period of the force be greater than the critical period, no significant local disturbance can result, because the disturbance near the origin which the force tends to produce is carried away in both directions. But when the period of the force is less than the critical period the local disturbance mounts up continually, tending towards its permanent state.
Suppose now the disturbing force, after having acted long enough to bring the motion into its permanent state, were then to cease. In the first case there would indeed be a change of motion in the neighbourhood of the origin; but as the excursions of the masses would be but small, for the reason already mentioned, the effect of the change would be quite insignificant. But in the second case the disappearance of the force would leave the masses in the neighbourhood of the origin in a condition of displacement or motion which is not, as in the former cane, insignificant, and which may be thought of as an initial disturbance in a system now left to itself. This disturbance would gradually widen out so as to involve a continually increasing group of masses, and the variation of the motion as at a given moment we proceed along the string would become less and less sharp as the time progresses, so that the disturbance if harmonically resolved would give a result in which the elements of the resolution corresponding to longer periods would acquire an increasing relative importance.
The general analogy of these dynamical results to the phenomena of fluorescence will I think be readily perceived. The periodic force acting on one of the masses of our loaded string is analogous to the action of the incident ethereal vibrations on a constituent part of a complex molecule or molecular group. The considerable but finite regularity of the disturbing force is analogous to what we must suppose to be going on as regards the ethereal vibrations in a small portion of a nearly pure spectrum. The agitation of the masses when the disturbing force ceases and the loaded string is left to itself is ana-logons to the agitation of the excited molecules when one series of regular incident ethereal vibrations comes to an end and is replaced by another such series,